Splice ./universe directory into ./
Manually merging: - README.md: I added the description from universe/README.md into the heading of dotfiles/README.md. - .envrc: dotfiles/.envrc was a superset of universe/.envrc - .gitignore: Adding some of the ignored patterns from universe/.gitignore to dotfiles/.gitignore Everything else here should be a simple rename.
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								data_structures_and_algorithms/optimal-stopping.py
									
										
									
									
									
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							|  | @ -0,0 +1,49 @@ | |||
| from random import choice | ||||
| from math import floor | ||||
| 
 | ||||
| # Applying Chapter 1 from "Algorithms to Live By", which describes optimal | ||||
| # stopping problems. Technically this simulation is invalid because the | ||||
| # `candidates` function takes a lower bound and an upper bound, which allows us | ||||
| # to know the cardinal number of an individual candidates. The "look then leap" | ||||
| # algorithm is ideal for no-information games - i.e. games when upper and lower | ||||
| # bounds aren't known. The `look_then_leap/1` function is ignorant of this | ||||
| # information, so it behaves as if in a no-information game. Strangely enough, | ||||
| # this algorithm will pick the best candidate 37% of the time. | ||||
| # | ||||
| # Chapter 1 describes two algorithms: | ||||
| # 1. Look-then-leap: ordinal numbers - i.e. no-information games. Look-then-leap | ||||
| #    finds the best candidate 37% of the time. | ||||
| # 2. Threshold: cardinal numbers - i.e. where upper and lower bounds are | ||||
| #    known. The Threshold algorithm finds the best candidate ~55% of the time. | ||||
| # | ||||
| # All of this and more can be studied as "optimal stopping theory". This applies | ||||
| # to finding a spouse, parking a car, picking an apartment in a city, and more. | ||||
| 
 | ||||
| 
 | ||||
| # candidates :: Int -> Int -> Int -> [Int] | ||||
| def candidates(lb, ub, ct): | ||||
|     xs = list(range(lb, ub + 1)) | ||||
|     return [choice(xs) for _ in range(ct)] | ||||
| 
 | ||||
| 
 | ||||
| # look_then_leap :: [Integer] -> Integer | ||||
| def look_then_leap(candidates): | ||||
|     best = candidates[0] | ||||
|     seen_ct = 1 | ||||
|     ignore_ct = floor(len(candidates) * 0.37) | ||||
|     for x in candidates[1:]: | ||||
|         if ignore_ct > 0: | ||||
|             ignore_ct -= 1 | ||||
|             best = max(best, x) | ||||
|         else: | ||||
|             if x > best: | ||||
|                 print('Choosing the {} candidate.'.format(seen_ct)) | ||||
|                 return x | ||||
|         seen_ct += 1 | ||||
|     print('You may have waited too long.') | ||||
|     return candidates[-1] | ||||
| 
 | ||||
| 
 | ||||
| candidates = candidates(1, 100, 100) | ||||
| print(candidates) | ||||
| print(look_then_leap(candidates)) | ||||
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